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An Input–Output Approach to Anti-windup Design for Sampled-Data Systems with Time-Varying Delay

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Abstract

A methodology for designing anti-windup compensators is investigated, for sampled-data systems with delays and actuator saturation. More precisely, criteria for the existence of an anti-windup compensator that ensure simultaneously stability and an \(H_{\infty }\) norm bound in closed-loop are developed, thanks to the use of a three-term approximation of the delays, of the scaled small gain theorem, and of a Wirtinger-based inequality. The criteria are in the form of a set of linear matrix inequalities: an optimization algorithm is proposed to maximize the estimated domain of attraction that can be easily implemented. Some simulation examples are also provided to demonstrate the superiority of the proposed approach.

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References

  1. A. Arbi, F. Charif, C. Aouiti, A. Touati, Dynamics of new class of Hopfield neural networks with time-varying and distributed delays. Acta Math. Sci. 36(3), 891–912 (2016)

    MathSciNet  MATH  Google Scholar 

  2. A. Arbi, J. Cao, Pseudo-almost periodic solution on time-space scales for a novel class of competitive neutral-type neural networks with mixed time-varying delays and leakage delays. Acta Math. Sci. 46(2), 719–745 (2017)

    Google Scholar 

  3. A. Arbi, J. Cao, A. Alsaedi, Improved synchronization analysis of competitive neural networks with time-varying delays. Nonlinear Anal. Model. Control 23(1), 82–102 (2018)

    MathSciNet  MATH  Google Scholar 

  4. A. Arbi, Dynamics of BAM neural networks withmixed delays and leakage time-varying delays in the weighted pseudo almost periodic on time-space scales. Math. Methods Appl. Sci. 41(3), 1230–1255 (2018)

    MathSciNet  MATH  Google Scholar 

  5. S.A. Belamfedel, E.H. Tissir, N. Chaibi, Active queue management based feedback control for TCP with successive delays in single and multiple bottleneck topology. Comput. Commun. 117, 58–70 (2018)

    Google Scholar 

  6. F.A. Bender, Delay dependent antiwindup synthesis for time delay systems. Int. J. Intell. Control Syst. 18(1), 1–9 (2013)

    Google Scholar 

  7. Y.Q. Cao, Y.Y. Sun, X.Y. Wang, Anti-windup compensator gain design for time-delay systems with constraints. Acta Autom. Sin. 32(1), 1–8 (2006)

    MathSciNet  Google Scholar 

  8. Y. Chen, Y. Li, S. Fei, Anti-windup design for time-delay systems via generalised delay-dependent sector conditions. IET Control Theory Appl. 11(10), 1634–1641 (2017)

    MathSciNet  Google Scholar 

  9. J.M.G. Da Silva, G. Garcia, Anti-windup design for time-delay systems subject to input saturation-an LMI-based approach. Eur. J. Control 12(6), 622–634 (2006)

    MathSciNet  MATH  Google Scholar 

  10. Z. Du, Z. Qin, H. Ren, Z. Lu, Fuzzy robust \(H_{\infty }\) sampled-data control for uncertain nonlinear systems with time-varying delay. Int. J. Fuzzy Syst. 19(5), 1417–1429 (2016)

    MathSciNet  Google Scholar 

  11. A. Ech-charqy, M. Ouahi, E.H. Tissir, Delay-dependent robust stability criteria for singular time-delay systems by delay-partitioning approach. Int. J. Syst. Sci 39(4), 2957–2967 (2018)

    MathSciNet  Google Scholar 

  12. H. El Aiss, A. Hmamed, A. El Hajjaji, Improved stability and \(H_{\infty }\) performance criteria for linear systems with interval time-varying delays via three terms approximation. Int. J. Syst. Sci. 48(16), 3450–3458 (2017)

    MathSciNet  MATH  Google Scholar 

  13. H. El Aiss, H. Rachid, A. Hmamed, A. El Hajjaji, Approach to delay-dependent robust stability and stabilisation of delta operator systems with time-varying delays. IET Control Theory Appl. 12(6), 786–792 (2018)

    MathSciNet  Google Scholar 

  14. N. El Fezazi, F. El Haoussi, E.H. Tissir, F. Tadeo, Delay dependent anti-windup synthesis for time-varying delay systems with saturating actuators. Int. J. Comput. Appl. 111(1), 1–6 (2015)

    Google Scholar 

  15. N. El Fezazi, O. Lamrabet, F. El Haoussi, E.H. Tissir, T. Alvarez, F. Tadeo, Proceedings of the International Conference on Systems and Control (ICSC). Robust controller design for congestion control in TCP/IP routers, Marrakesh, Morocco (2016), p. 243–249

  16. N. El Fezazi, E.H. Tissir, F. El Haoussi, T. Alvarez, F. Tadeo, Control Based on Saturated Time-Delay Systems Theory of Mach Number in Wind Tunnels. Circuits, Systems and Signal Processing (2017)

  17. N. El Fezazi, F. El Haoussi, E.H. Tissir, T. Alvarez, F. Tadeo, Robust stabilization using a sampled-data strategy of uncertain neutral state-delayed systems subject to input limitations. Int. J. Appl. Math. Comput. Sci. 28, 111–122 (2018)

    MathSciNet  MATH  Google Scholar 

  18. F. El Haoussi, E.H. Tissir, Delay and its time-derivative dependent robust stability of uncertain neutral systems with saturating actuators. Int. J. Autom. Comput. 7(4), 455–462 (2010)

    Google Scholar 

  19. F. El Haoussi, E.H. Tissir, A. Hmamed, F. Tadeo, Stabilization of neutral systems with saturating actuators. J. Control Sci. Eng. (2012). https://doi.org/10.1155/2012/823290

    Article  MathSciNet  MATH  Google Scholar 

  20. E. Fridman, U. Shaked, Input–output approach to stability and \(L_{2}\)-gain analysis of systems with time-varying delays. Syst. Control Lett. 55(12), 1041–1053 (2007)

    MATH  Google Scholar 

  21. Y. He, Q.G. Wang, L. Xie, C. Lin, Further improvement of free weighting matrices technique for systems with time-delay. IEEE Trans. Autom. Control 52(2), 293–299 (2007)

    MathSciNet  MATH  Google Scholar 

  22. A. Hmamed, H. El Aiss, A. El Hajjaji, Stability analysis of linear systems with time varying delay: an input output approach. IEEE 54th Annual Conference Decision and Control (CDC), Osaka, Japan (2015), p. 15–18

  23. J. Hu, W.P. Li, Theory of Ordinary Differential Equations Existence (Department of Mathematics, The Hong Kong University of Science and Technology, Uniqueness and Stability, 2005)

  24. O. Lamrabet, N. El Fezazi, F. El Haoussi, E.H. Tissir, Using input delay approach for synthesizing an anti-windup compensator to AQM in TCP/IP networks. International Conference on Advanced Technologies, Signal and Image Processing, Fez, Morocco (2017). https://doi.org/10.1109/ATSIP.2017.8075573

  25. O. Lamrabet, E.H. Tissir, F. El Haoussi, Anti-windup compensator synthesis for sampled-data delay systems. Circuits Syst. Signal Process (2018). https://doi.org/10.1007/s00034-018-0971-9

    Article  Google Scholar 

  26. O. Lamrabet, A. Ech-charqy, E.H. Tissir, F. El Haoussi, Sampled data control for Takagi–Sugeno fuzzy systems with actuator saturation. Proc. Comput. Sci. 148, 448–454 (2019)

    Google Scholar 

  27. K. Liu, E. Fridman, Wirtinger’s inequality and Lyapunov-based sampled-data stabilization. Automatica 48(1), 102–108 (2012)

    MathSciNet  MATH  Google Scholar 

  28. Y. Liu, M. Li, Improved robust stabilization method for linear systems with interval time-varying input delays by busing Wirtinger inequality. ISA Trans. 56, 111–122 (2015). https://doi.org/10.1016/j.isatra.2014.12.008

    Article  Google Scholar 

  29. A. Manitius, Feedback controllers for a wind tunnel model involving a delay: analytical design and numerical simulation. IEEE Trans. Autom. Control 29(12), 1058–1068 (1984)

    MathSciNet  Google Scholar 

  30. M.J. Park, O.M. Kwon, J.H. Park, S.M. Lee, E.J. Cha, Stability of time-delay systems via wirtinger-based double integral inequality. Automatica 55, 204–208 (2015)

    MathSciNet  MATH  Google Scholar 

  31. H. Rachid, O. Lamrabet, E.H. Tissir, Stabilization of delta operator systems with actuator saturation via anti-windup compensator. Symmetry 11, 1084–1093 (2019). https://doi.org/10.3390/sym11091084

    Article  Google Scholar 

  32. R. Sakthivel, M. Joby, P. Shi, K. Mathiyalagan, Robust reliable sampled-data control for switched systems with application to flight control. Int. J. Syst. Sci. 47(15), 3518–3528 (2016)

    MathSciNet  MATH  Google Scholar 

  33. S. Santra, H.R. Karimi, R. Sakthivel, A.S. Marshal, Dissipative based adaptive reliable sampled-data control of time-varying delay systems. J Franklin Inst. 14(1), 39–50 (2016)

    Google Scholar 

  34. S. Tarbouriech, J.M.G. Da Silva, G. Garcia, Delay-dependent anti-windup loops for enlarging the stability region of time-delay systems with saturating inputs. J. Dyn. Syst. Meas. Control 125(2), 265–267 (2003)

    Google Scholar 

  35. E.H. Tissir, Delay-dependent robust stability of linear systems with non-commensurate time varying delays. Int. J. Syst. Sci. 38, 749–757 (2007)

    MathSciNet  MATH  Google Scholar 

  36. E.H. Tissir, Delay-dependent robust stabilization for systems with uncertain time varying delay. J. Dyn. Syst. Meas. Control 132(5), 054504 (2010)

    Google Scholar 

  37. Y. Wu, B. Jiang, N. Lu, A descriptor system approach for estimation of incipient faults with application to high-speed railway traction devices. IEEE Trans. Syst. Man Cybern. Syst. (2017). https://doi.org/10.1109/TSMC.2017.2757264

    Article  Google Scholar 

  38. H. Yang, Z. Li, C. Hua, Z. Liu, Stability analysis of delta operator systems with actuator saturation by a saturation dependent Lyapunov function. Circuits Syst. Signal Process. (2015). https://doi.org/10.1007/s00034-014-9876-4

    Article  MathSciNet  MATH  Google Scholar 

  39. L. Zhao, H. Gao, H.R. Karimi, Robust stability and stabilization of uncertain T–S fuzzy systems with time varying delay: an input–output approach. IEEE Trans. Fuzzy Syst. 21(5), 883–897 (2013)

    Google Scholar 

  40. T. Zoulagh, H. El Aiss, A. Hmamed, A. El Hajjaji, \(H_{\infty }\) filter design for discrete time-varying delay systems: three-term approximation approach. IET Control Theory Appl. 12(2), 254–262 (2018)

    MathSciNet  Google Scholar 

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Acknowledgements

Prof. Fernando Tadeo is funded by Conserjeria de Educacion, Junta de Castilla y Leon with European Regional Development Funds (Grant No. CLU 2017-09 and UIC 233).

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Authors and Affiliations

  1. LESSI, Department of Physics, Faculty of Sciences Dhar El Mehraz, University Sidi Mohammed Ben Abdellah, BP 1796, Fes-Atlas, Morocco

    Ouarda Lamrabet, Khadija Naamane, El Houssaine Tissir & Fatima El Haoussi

  2. Department of Systems Engineering and Automatic Control and Institute of Sustainable Processes, University of Valladolid, 47005, Valladolid, Spain

    Fernando Tadeo

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  1. Ouarda Lamrabet
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  2. Khadija Naamane
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  3. El Houssaine Tissir
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  4. Fatima El Haoussi
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  5. Fernando Tadeo
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Correspondence to Fernando Tadeo.

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Lamrabet, O., Naamane, K., Tissir, E.H. et al. An Input–Output Approach to Anti-windup Design for Sampled-Data Systems with Time-Varying Delay. Circuits Syst Signal Process 39, 4868–4889 (2020). https://doi.org/10.1007/s00034-020-01414-w

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